Greenway was named in honour of Francis Howard Greenway (1777-1837). Francis Greenway was a Colonial architect and arrived in Sydney as a transportee in 1814. He worked as an architectural adviser on public works from 1814-1815 and was later appointed Civil Architect and Assistant Engineer in 1816. Greenway supervised the construction of a number of public buildings. Howard Greenway also adapted designs and methods to suit the Australian climate.